Question

If a, b, c are three non-coplanar vectors such that volume of parallelopiped formed with a, b, c, as coterminous edges is equal to volume of parallelopiped formed with $a\times b,b\times c,c\times a$ as coterminous edges, then:

• A. $\left[abc\right]=0$
• B. $\left[abc\right]=1$
• C. $\left[abc\right]=-1$
• D. $\left[abc\right]ϵ(-1,1)$

Answer 1

Answer: (B), (C)

$\left[abc\right]=1$
$\left[abc\right]=-1$

Given $\left[abc\right]\ne 0$
Also $\left|\left[abc\right]\right|=[b\times cc\times aa\times b]$ or $\left|\left[abc\right]\right|={\left[abc\right]}^2$
Thus, $\left[abc\right]=\pm 1$